What is the integral from 2 to 1 of-4x^{-3} ?

The integral from 2 to 1 of-4x^{-3} is 3/2

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integral from 2 to 1 of-4x^{-3}

\int_{2}^{1} - 4 x^{- 3} d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{2}^{1} - 4 x^{- 3} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{2} - 4 x^{- 3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- 4 \cdot \int_{1}^{2} x^{- 3} d x)

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{2}

= - (- 4 [- \frac{1}{2 x ^{2}}]_{1}^{2})

Simplify

= 4 [- \frac{1}{2 x ^{2}}]_{1}^{2}

Compute the boundaries:

\frac{3}{8}

= 4 \cdot \frac{3}{8}

Simplify

= \frac{3}{2}

\int \frac{x ^{7}}{( 2 - x ^{8} ) ^{2}} d x

10000 y^{^{''}} - 81 y = 0, y (0) = 1, y^{^{'}} (0) = 3

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

y^{^{'}} = - k y^{3}

\int (\frac{1}{x} + cot (x) - sec (x)) d x

What is the integral from 2 to 1 of-4x^{-3} ?
The integral from 2 to 1 of-4x^{-3} is 3/2